What does Luke 10:11 mean?

Again, Jesus reiterates the same instructions He previously gave the Twelve (Luke 9:5). In Luke 10:4–6, Jesus describes the messengers' accommodations. He does not tell them to only stay in homes of Jews who practice the Law. He tells them to stay with those who respond in peace. Similarly, they are not to worry about the ceremonial cleanness of the food their hosts give them (Luke 10:8).

Now, Jesus says something similar for the whole town. To shake the dust off their feet is a sign the town is unclean. The power in the action is not that the disciples would make themselves purified from the uncleanness of the village but the declaration, itself, that the village is unclean—a pronouncement of shame. No matter their response, they will see the kingdom of God. If they respond in peace, they will receive healing—a blessing of God's kingdom. If they reject the message, they will receive judgment.

Jesus also tells the disciples to affirm that the kingdom of God has come near. When someone accepts their words, they are to say "The kingdom of God has come near to you" [emphasis added] (Luke 10:9). If they reject their message, the kingdom will still come, but not to their benefit. They will be judged even more harshly than the Gentiles who do not claim to worship God and do not receive the signs of God's kingdom (Luke 10:12–15).

Of course, if the town repents later, they will be blessed. The problem is, the villagers are not rejecting the disciples, they are rejecting the message the disciples share, which means they reject Jesus (Luke 10:16). The villagers could repent, but it's unlikely they will. When Jesus told the Twelve to follow this practice, James and John preferred to call fire down from heaven, instead (Luke 9:51–56). Paul and Barnabas, however, find this act gets the message across so well that those they judge in one city follow them to another and try to stone Paul to death (Acts 13:50–52; 14:19).